[Proof of Lemma REF ]
From \((S36)\)  of [1]} we have,
\(\frac{dv_i}{dt} & = \eta _v \left[ \sum _{n=1}^{M} v_n ^* I_2(i,n) -\sum _{j=1}^{K} v_j I_2(i,j) \right] \\& = \eta _v \arcsin \frac{1}{2} \left[ v^* -\sum _{j \in G_{n}} v_j \right]\) 
